If a matrix has 28 elements,
Question:

If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

Solution:

For a given matrix of order m x n, it has mn elements, where m and n are natural numbers.

Here we have, m x n = 28

(m, n) = {(1, 28), (2, 14), (4, 7), (7, 4), (14, 2), (28, 1)}

So, the possible orders are 1 x 28, 2 x 14, 4 x 7, 7 x 4, 14 x 2, 28 x 1.

Also, if it has 13 elements, then m x n = 13

(m, n) = {(1, 13), (13, 1)}

Thus, the possible orders are 1 x 13, 13 x 1.

$\left[\begin{array}{ccc}a & 1 & x \\ 2 & \sqrt{3} & x^{2}-y \\ 0 & 5 & \frac{-2}{5}\end{array}\right]$